A ballhead makes it easier to orient the camera in odd or unusual positions, but that's also its drawback. Unless it has a pano base it is difficult to adjust the camera in one direction without disturbing its orientation on other axes. If you tilt up, you can inadvertently cant the camera sideways. A panhead makes it easy to adjust tilt without affecting cant or pan settings, and vice versa. But that means that you must adjust them separately, which can take longer.

A sturdy ballhead is the choice of most nature photographers because it's very quick and intuitive to use for getting the camera just where you want it. Pan/tilt heads are intrinsically more precise, but take longer because you have to independently adjust and tighten each axis. Those projecting handles also tend to snag on vegetation when you're slogging through brush. You pays your money and takes your chances.

Can somebody tell me the advantage of a ballhead over a panhead. I just purchased my first tripod which comes with a panhead, but would like to know if it's advantageous to get a ballhead as well. I'm new to this equipment end of photography. Thanks.

Because I have limited finances and can't afford Gitzo right now, here's what I just purchased for my Canon EOS 20D and EF-S 17-85mm lens. I did get a ballhead: